x^2-27x+134=0

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Solution for x^2-27x+134=0 equation: 


Simplifying
x2 + -27x + 134 = 0

Reorder the terms:
134 + -27x + x2 = 0

Solving
134 + -27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-134' to each side of the equation.
134 + -27x + -134 + x2 = 0 + -134

Reorder the terms:
134 + -134 + -27x + x2 = 0 + -134

Combine like terms: 134 + -134 = 0
0 + -27x + x2 = 0 + -134
-27x + x2 = 0 + -134

Combine like terms: 0 + -134 = -134
-27x + x2 = -134

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = -134 + 182.25

Reorder the terms:
182.25 + -27x + x2 = -134 + 182.25

Combine like terms: -134 + 182.25 = 48.25
182.25 + -27x + x2 = 48.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -13.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + -13.5 = 6.946221995

Simplifying
x + -13.5 = 6.946221995

Reorder the terms:
-13.5 + x = 6.946221995

Solving
-13.5 + x = 6.946221995

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 6.946221995 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 6.946221995 + 13.5
x = 6.946221995 + 13.5

Combine like terms: 6.946221995 + 13.5 = 20.446221995
x = 20.446221995

Simplifying
x = 20.446221995


Subproblem 2
x + -13.5 = -6.946221995

Simplifying
x + -13.5 = -6.946221995

Reorder the terms:
-13.5 + x = -6.946221995

Solving
-13.5 + x = -6.946221995

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -6.946221995 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -6.946221995 + 13.5
x = -6.946221995 + 13.5

Combine like terms: -6.946221995 + 13.5 = 6.553778005
x = 6.553778005

Simplifying
x = 6.553778005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.446221995, 6.553778005}

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